Interpolation is the process of estimating the intermediate value of a continuous event from discrete samples. Interpolation is used extensively in digital image processing to magnify or reduce images and to correct spatial distortions. Several interpolation functions have been used for image resampling (Maeland, E., On the Comparison of Interpolation Methods, IEEE Transactions on Medical Imaging, Vol. 7, No. 3, September 1988, pp. 213-217). It is widely accepted that image quality can be improved by resampling using a high-resolution cubic convolution function as compared to the nearest neighbor, linear, or cubic B-spline functions. (Keys, R. G., Cubic Convolution Interpolation for Digital Image Processing, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-29, No. 6, December 1981). For this reason, cubic spline interpolation has become a widely used method in digital image processing. However, cubic spline interpolation generates objectionable image artifacts under a number of real world imaging conditions.
Lien, et. al., Lien, Sheue-Ling, et. al. Method and Apparatus for Shading Images, U.S. Pat. No. 5,063,375, Nov. 5, 1991 disclosed a method for generating shaded images based on surface normal calculation. Both Kimura, et. al., Apparatus to Improve Image Enlargement or Reduction by Interpolation. U.S. Pat. No. 5,301,226, Apr. 5, 1994 and Potter, et. al., Method and Apparatus for Enhancing Frequency Domain Analysis. U.S. Pat. No. 5,473,555, Dec. 5, 1995, present methods of interpolation based on frequency domain analysis. Takayama, et. al., Hybrid Interpolation and Non-Interpolation Method and Apparatus for Image Enlarging and Contraction. U.S. Pat. No. 5,400,154, Mar. 21, 1995 present a hybrid method to image interpolation. Each of these methods is disadvantageous.
Hrytzak, et. al., Method and Apparatus for Adaptively Interpolating a Digital Image. U.S. Pat. No. 5,327,257, Jul. 5, 1994, present an adaptive method for interpolation based on a system which switches between sets of precomputed kernels on the basis of image data. The drawbacks of precomputed kernels are the same as those of cubic convolution and linear averaging discussed above--these techniques being based on precomputed kernels.